The 1/4" to 1/8" headphone adapter is fine, just be sure to be careful with the headphone volume control since typical headsets tend to be comparatively sensitive.
But the mic requires a special adapter for converting phantom power on XLR to plugin power TRS.
These days there are oodles of "instrument microphones" with some phantom-to-plugin-power adapter for use with XLR, and for use with wireless transmitters without XLR. Because there are wireless transmitters with 1/8" phone plugs, you'll also find adapters converting XLR phantom power to plugin power on 1/8" phone plugs.
A brand item would be "Røde VXLR+" (the plus sign is crucially important here!), a discounter house brand item would be "t.bone CC 100 EW". There are various other offers with a different degree of quality (some containing a balancing transformer) but keep in mind what you are dealing with here: integrated headset mics are usually cheap stuff intended for cheap inputs. A superior balancing adapter allowing to use a 30m balanced XLR cable run from a stagebox is going to be ridiculously overengineered for almost all applications and headsets.